Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON):

Solution:
from bisect import bisect_left as bisect

def trigen(n):
    k = 1
    while True:
        tmp = k * (k + 1) / 2
        if tmp > n:
            raise StopIteration
        yield tmp
        k += 1

n = int(raw_input())
trinums = list(trigen(n))
flag = False
l = len(trinums)
for i in xrange(l):
    leftpart = n - trinums[i]
    j = bisect(trinums, leftpart)
    if j < l and trinums[j] == leftpart:
        flag = True
        break
print 'YES' if flag else 'NO'